In general, the number of ways in which a set of LIOMs can be arranged is very large, and, therefore, the calculation of all LIOMs is a complicated task practically.
It was first pointed out that a complete set of LIOMs for a finite-size system can be obtained via labeling the eigenstates of the system by their corresponding LIOM-eigenvalues uniquely [1]}, [2]}.
Then, it was suggested to construct LIOMs (which do not form a complete basis) by computing an infinite-time average of initially local operators [3]}, [4]}.
In this regard, various approaches like using Monte-Carlo stochastic method [5]}, exact diagonalization techniques [6]}, [7]}, [8]}, [9]} , and tensor networks [10]}, [11]}, [12]}, [13]} have
been developed.
